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.

Effects of kinetic and transport phenomena on thermal explosion and oscillatory behaviour in a spherical reactor with mixed convection

“…The finite-element solver Fastflo 23 was used with an algorithm as described previously. 7,20,[24][25][26] The method of Picard of successive approximations was employed for linearisation, combined with a backward Euler time-stepping scheme, and the momentum and continuity equations were coupled using the Augmented-Lagrangian method. 23 Owing to the axisymmetric geometry, a semi-circular mesh of about 7500 elements was applied and a timestep of 0.01 s was used.…”

Exploding Chemical Gardens: A Phase‐Change Clock Reaction

“…But it is inarguable that the classic clock reactions are timers: they have an induction period that may be very long followed by a sharp change, often a color change, at a given moment, and this induction time can be controlled and predicted by altering the quantities of reagents. Examples in gaseous combustion have shown the dependence of the induction time before explosion on the transport rates of chemicals and heat . In the case of our scenario, the concept of a chemical clock is based upon the chemical‐garden reaction acting as a timer, the period of which we can control.…”