Travelling waves and oscillations in Sal'nikov's combustion reaction in a compressible gas.

Rhys A. Paul, Lawrence K. Forbes

Abstract


We consider a two-step Sal’nikov reaction scheme occurring within a compressible viscous gas. The first step of the reaction may be either endothermic or exothermic, while the second step is strictly exothermic. Energy may also be lost from the system due to Newtonian cooling. An asymptotic solution for temperature perturbations of small amplitude is presented using the methods of strained coordinates and multiple scales, and a travelling wave solution with a sech-squared profile is derived. The method of lines is then used to approximate the full system with a set of ordinary differential equations, which are integrated numerically to track accurately the evolution of the reaction front. This numerical method is used to verify the asymptotic solution and investigate behaviours under different conditions. Using this method, temperature waves progressing as pulsatile fronts are detected at appropriate parameter values.


doi:10.1017/S1446181114000479

Keywords


Sal’nikov reaction; combustion; solitons; pulsatile waves; strained coordinates; multiple scales; method of lines



DOI: http://dx.doi.org/10.21914/anziamj.v56i0.8118



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ANZIAM Journal, ISSN 1446-8735, copyright Australian Mathematical Society.