Combustion waves in a model with chain branching reaction and their stability

TL;DR

This paper investigates the properties and stability of combustion wave solutions in a two-step chain branching reaction model, revealing similarities and differences with one-step models, especially near extinction conditions.

Contribution

It provides a detailed numerical and analytical study of combustion waves in an adiabatic two-step chain branching model, highlighting stability and extinction behaviors.

Findings

Combustion waves exhibit residual fuel and potential extinction similar to nonadiabatic models.

Near extinction, flame velocity approaches zero, forming a standing wave.

Differences between one-step and two-step models are significant near extinction conditions.

Abstract

In this paper the travelling wave solutions in the adiabatic model with two-step chain branching reaction mechanism are investigated both numerically and analytically in the limit of equal diffusivity of reactant, radicals and heat. The properties of these solutions and their stability are investigated in detail. The behaviour of combustion waves are demonstrated to have similarities with the properties of nonadiabatic one-step combustion waves in that there is a residual amount of fuel left behind the travelling waves and the solutions can exhibit extinction. The difference between the nonadiabatic one-step and adiabatic two-step models is found in the behaviour of the combustion waves near the extinction condition. It is shown that the flame velocity drops down to zero and a standing combustion wave is formed as the extinction condition is reached. Prospects of further work are also discussed.