Critical ignition conditions in exothermically reacting systems for arbitrary reaction kinetics

Abstract

In this work, a universal method for determination of the critical ignition conditions taking into account the reactant consumption is proposed. Based on the analysis of the phase trajectories equation, the equation for maximal temperatures of exothermic reactions was obtained. In this case, the asymptotic criterion of ignition is determined by the impossibility of slow reaction mode realization with low value of maximum temperature. The method allows demarcating the regions of low- and high-temperature modes of exothermic reactions and to establish the criteria of transition to the region of high-temperature modes. The corresponding parametric diagrams can be characterized as the bifurcation ones (bistability). It was found that the region of thermal explosion (TE) existence is bounded by the classical TE conditions from below and by the degeneration conditions from above. The comparison of analytical calculation results with the results of numerical calculation gives a satisfactory agreement.