NUMERICAL STUDY OF AN ALUMINOTHERMIC REACTION BY A FOURTH-ORDER FINITE DIFFERENCE SCHEME WITH THE REACTION RATE MODELED AS CONSTANT AND BY THE N-ORDER METHOD

Resumo

Aluminothermic reactions have been widely applied in rail welding, pyrotechnics, and mate-
rial synthesis, as they are highly exothermic. However, they are not easily modeled since they involve

condensed phases, hardly result in gas products, and produce heterogeneous combustion waves where

no thermodynamic equilibrium condition is attained. Moreover, the reaction rate of these reactions de-
pends on particle sizes, oxidizer type, mixture ratios, and other physicochemical characteristics. So,

major studies about aluminothermic reactions have been experimental, and just a few authors have tried
to model the front propagation, shock generation and the kinetics of them. In this point of view, the
present study aims to model the aluminothermic reaction between hematite and aluminum by solving the

energy and mass conservation equations with a fourth-order finite difference scheme in space and first-
order forward scheme in time. As there are not enough experimental studies about the activation energy

and pre-exponential factor for this specific reaction, the reaction rate was modeled both as a constant
and by the n-order method, which considers the dependence of reaction rate on temperature and species

concentration and made it possible to observe the sensibility of these parameters. Moreover, the tem-
perature dependence of density, specific heat capacity and thermal conductivity were considered in the

model. The geometry and boundary conditions were based on experimental data from literature, which
successfully enabled validation of the mean temperature and velocity propagation of the reaction.