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One-dimensional nonlinear stability of pathological detonations

Sharpe, G.J. and Falle, S.A.E.G. (2000) One-dimensional nonlinear stability of pathological detonations. Journal of Fluid Mechanics, 414. pp. 339-366. ISSN 0022-1120


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In this paper we perform high-resolution one-dimensional time-dependent numerical simulations of detonations for which the underlying steady planar waves are of the pathological type. Pathological detonations are possible when there are endothermic or dissipative effects in the system. We consider a system with two consecutive irreversible reactions A[rightward arrow]B[rightward arrow]C, with an Arrhenius form of the reaction rates and the second reaction endothermic. The self-sustaining steady planar detonation then travels at the minimum speed, which is faster than the Chapman–Jouguet speed, and has an internal frozen sonic point at which the thermicity vanishes.

The flow downstream of this sonic point is supersonic if the detonation is unsupported or subsonic if the detonation is supported, the two cases having very different detonation wave structures. We compare and contrast the long-time nonlinear behaviour of the unsupported and supported pathological detonations. We show that the stability of the supported and unsupported steady waves can be quite different, even near the stability boundary. Indeed, the unsupported detonation can easily fail while the supported wave propagates as a pulsating detonation. We also consider overdriven detonations for the system. We show that, in agreement with a linear stability analysis, the stability of the steady wave is very sensitive to the degree of overdrive near the pathological detonation speed, and that increasing the overdrive can destabilize the wave, in contrast to systems where the self-sustaining wave is the Chapman–Jouguet detonation.

Item Type: Article
Copyright, Publisher and Additional Information: © Cambridge University Press
Institution: The University of Leeds
Academic Units: The University of Leeds > Faculty of Maths and Physical Sciences (Leeds) > School of Mathematics (Leeds) > Applied Mathematics (Leeds)
Depositing User: Repository Assistant
Date Deposited: 26 May 2006
Last Modified: 04 Jun 2014 15:27
Published Version: http://dx.doi.org/10.1017/S0022112000008697
Status: Published
Publisher: Cambridge University Press
Refereed: Yes
Identification Number: 10.1017/S0022112000008697
URI: http://eprints.whiterose.ac.uk/id/eprint/1235

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