OpenMP parallel computing of 2D TiC combustion synthesis process using an explicit finite-volume scheme

Abstract

This paper analyzes from a numerical point of view the ignition and propagation of the combustion front during the exothermic TiC combustion synthesis of a material made of pressed titanium and carbide particles when thermophysical properties are either assumed constant or temperature and conversion rate dependent. A two-dimensional cylindrical geometry is considered. The heat supply is prescribed on one, two or three sides of the physical domain. A one-step kinetics is used to describe the reaction Ti+C→TiC in a solid phase and leads to the computation of the conversion rate. A coupling with a non-linear heat equation which takes into account the heat generated by the exothermic kinetics and the two allotropic phase-changes is considered. An explicit finite-volume discretization of the coupled system is constructed and analyzed. Time-step’s stability condition is given for a general expression of the thermo-physical characteristics. A discrete maximum principle is reported. Open MP API was used to parallelize the numerical software written in C. An average speedup of three was obtained on an intel quad-core processor i7-2600. The ignition time and the fraction of unreacted material are systematically computed and compared for several heat supply scenario.