An implicit finite volume discretization for the multidimensional numerical simulation of TiC combustion synthesis

摘要

A reaction–diffusion mathematical modelling of titanium–carbide combustion synthesis from a mixture of titanium and carbide reactive powders by self-propagating high temperature synthesis process is presented. This modelling results in the coupling between a nonlinear parabolic equation expressing the enthalpy balance of the system with nonhomogeneous Neumann boundary conditions and a nonlinear differential equation describing the exothermic chemical reaction in the system. In order to analyze by numerical simulation the influence of the boundary conditions over the ignition and propagation of the combustion front in the reactive mixture, an implicit finite volume scheme is constructed for the discretization of the governing equations of the process. An error estimate for the discrete approximation of the parabolic equation is established. A positivity property of both the sparse matrix arising in the discretization of the reaction–diffusion equation and the discrete approximation of the differential equation is presented. Detailed unsteady numerical simulations in one and two spatial dimensions of the influence of radiative boundary conditions over induction time and ignition transients are reported and discussed.