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Homogeneous explosion and shock initiation for a three-step chain-branching reaction model

Sharpe, G.J. and Maflahi, N. (2006) Homogeneous explosion and shock initiation for a three-step chain-branching reaction model. Journal of Fluid Mechanics, 566. pp. 163-194. ISSN 0022-1120

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Abstract

The role of chain-branching cross-over temperatures in shock-induced ignition of reactive materials is studied by numerical simulation, using a three-step chainbranching reaction model. In order to provide insight into shock initiation, the simpler problem of a spatially homogeneous explosion is first considered. It is shown that for ratios of the cross-over temperature to the initial temperature, T-B, sufficiently less than unity, the homogeneous explosion can be quantitatively described by a widely used two-step model, while for T-B sufficiently above unity the homogeneous explosion can be effectively described by the standard one-step model. From the matchings between these homogeneous-explosion solutions, the parameters of the reduced models are identified in terms of those of the three-step model. When T-B is close to unity, all the reactions of the three-step model have a leading role, and hence in this case the model cannot be reduced further. In the case of shock initiation, for T-B (which is now the ratio of the cross-over temperature to the initial shock temperature) sufficiently below unity, the three-step solutions are qualitatively described by those of the matched two-step model, but there are quantitative differences due to the assumption in the reduced model that a purely chain-branching explosion occurs instantaneously. For T-B sufficiently above unity, the matched one-step model is found to effectively describe the way in which the heat release and fluid dynamics couple. For T-B close to unity, the competition between chain branching and chain termination is important from the outset. In these cases the speed at which the forward moving explosion wave that emerges from the piston is sensitive to T-B, and changes from supersonic to subsonic for a value of T-B just below unity.

Item Type: Article
Copyright, Publisher and Additional Information: Copyright © 2006 Cambridge University Press. Reproduced in accordance with the publisher's self-archiving policy.
Institution: The University of Leeds
Academic Units: The University of Leeds > Faculty of Engineering (Leeds) > School of Mechanical Engineering (Leeds) > Institute of Engineering Thermofluids, Surfaces & Interfaces (iETSI) (Leeds)
Depositing User: Repository Officer
Date Deposited: 31 Mar 2008 09:49
Last Modified: 06 Jun 2014 08:30
Published Version: http://dx.doi.org/10.1017/S0022112006001844
Status: Published
Publisher: Cambridge University Press
Refereed: Yes
Identification Number: 10.1017/S0022112006001844
URI: http://eprints.whiterose.ac.uk/id/eprint/3718

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