Bridging the Gray and Yang, Sal'nikov and one-step, non-isothermal reaction schemes for oscillatory and explosive behaviour

Abstract

Explosions may occur as a result of thermal and branching effects in combustion processes. The aim of this work is to study the effects of chain branching and termination in a “Gray and Yang” three-step, chain-thermal reaction scheme, and the role of thermal diffusion and convection in determining the global behaviour. The response includes steady, exothermic combustion, oscillatory reaction and explosion. This was done by solving numerically the governing equations for the underlying kinetics and the heat transport, and analysing solutions for the limits at which each transport phenomenon dominates. Using scales to describe the different transport mechanisms, a 3D regime diagram is used to characterise the behaviour of the system. The results show how branching and heating by reaction enhance the oscillatory and explosive behaviour. The integration of a two-step Sal'nikov reaction scheme and a one-step reaction model in the Gray and Yang scheme is presented and the Frank-Kamenteskii and Semenov limits are identified on the regime diagram. Comparison is made with some experimental, numerical and analytical results.