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Travelling waves and oscillations in Sal'nikov's combustion reaction in a compressible gas
journal contribution
posted on 2023-05-18, 09:37 authored by Paul, RA, Lawrence ForbesLawrence ForbesWe 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 di fferential 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 di fferent conditions. Using this method, temperature waves progressing as pulsatile fronts are detected at appropriate parameter values.
History
Publication title
The ANZIAM JournalVolume
56Pagination
233-247ISSN
1446-1811Department/School
School of Natural SciencesPublisher
Australian Mathematics Publ Assoc IncPlace of publication
Mathematics Dept Australian National Univ, Canberra, Australia, Act, 0200Rights statement
Copyright 2015 Australian Mathematical SocietyRepository Status
- Restricted