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Travelling waves and oscillations in Sal'nikov's combustion reaction in a compressible gas
Citation
Paul, RA and Forbes, LK, Travelling waves and oscillations in Sal'nikov's combustion reaction in a compressible gas, The ANZIAM Journal, 56, (3) pp. 233-247. ISSN 1446-1811 (2015) [Refereed Article]
Copyright Statement
Copyright 2015 Australian Mathematical Society
DOI: doi:10.1017/S1446181114000479
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.
Item Details
Item Type: | Refereed Article |
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Keywords: | combustion, solitons, pulsatile waves, strained coordinates |
Research Division: | Mathematical Sciences |
Research Group: | Applied mathematics |
Research Field: | Dynamical systems in applications |
Objective Division: | Expanding Knowledge |
Objective Group: | Expanding knowledge |
Objective Field: | Expanding knowledge in the mathematical sciences |
UTAS Author: | Paul, RA (Dr Rhys Paul) |
UTAS Author: | Forbes, LK (Professor Larry Forbes) |
ID Code: | 100216 |
Year Published: | 2015 |
Web of Science® Times Cited: | 3 |
Deposited By: | Mathematics and Physics |
Deposited On: | 2015-05-07 |
Last Modified: | 2017-11-01 |
Downloads: | 0 |
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