The Unified Theory for Chain Branching Thermal Explosions with Dissociation-Recombination and Confinement Effects

Abstract

The complete time-history of a spatially homogeneous, constant volume model of self-initiated branched-chain explosion including high temperature dissociation arid recombination is examined. This model is motivated by characteristic chemical kinetic steps that are known to occur in H₂-O₂ systems. The kinetic scheme consists of high activation energy/initiation and chain-branching reactions, a zero activation energy gas phase termination reaction, a high activation energy dissociation reaction and a zero activation energy recombination reaction. Perturbation techniques and asymptotic methods are employed to find the transient response of the system temperature and species concentrations, when the high activation energy limit is valid. The chain branching explosion time is defined by very rapid growth of the chain carriers with little change in temperature. It is found that the slow initiation reactions delay the chain branching explosion time significantly compared to that found in simple reactive systems. Subsequently, we find the major part of the thermal explosion where the temperature rises to a maximum value higher than the adiabatic explosion temperature. This difference results from the compression heating in a finite volume. Then the temperature decreases to its final equilibrium value due to the endothermic dissociation reaction.