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Combustion waves in Sal'nikov's reaction scheme in a spherically symmetric gas
Citation
Paul, RA and Forbes, LK, Combustion waves in Sal'nikov's reaction scheme in a spherically symmetric gas, Journal of Engineering Mathematics, 101, (1) pp. 29-45. ISSN 0022-0833 (2016) [Refereed Article]
Copyright Statement
© Springer Science+Business Media Dordrecht 2016
DOI: doi:10.1007/s10665-016-9843-0
Abstract
We model a chemical reaction that proceeds according to Sal'nikov's combustion scheme in a spherically symmetric cloud of gas. The gas density, velocity, temperature and the concentration of intermediate reactant are all assumed to be small perturbations about a steady-state equilibrium, and linearised solutions to the governing partial differential equations are derived. We demonstrate that the behaviour of the solutions occurs in two different ways, depending on the value of a derived parameter which is defined in terms of various properties of the occurring reaction. When this parameter is zero, the solutions present as travelling waves, and exact solutions are found in terms of the initial perturbations to the chemical system. When this parameter is non-zero, solutions are found as integrals over a basis of spherical Bessel functions. A brief stability analysis of these solutions is also presented, and it is shown that the linear stability is dependent only on the same derived parameter. We then conclude by comparing the linear results to a numerical solution of the full non-linear problem, which verifies the accuracy of the linearised results.
Item Details
Item Type: | Refereed Article |
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Keywords: | combustion, waves, reaction scheme, gas flow |
Research Division: | Mathematical Sciences |
Research Group: | Applied mathematics |
Research Field: | Applied mathematics not elsewhere classified |
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: | 114886 |
Year Published: | 2016 |
Web of Science® Times Cited: | 1 |
Deposited By: | Mathematics and Physics |
Deposited On: | 2017-03-01 |
Last Modified: | 2017-11-01 |
Downloads: | 0 |
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