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Linear and nonlinear dynamics of cylindrically and spherically expanding detonation waves

Watt, S.D. and Sharpe, G.J. (2005) Linear and nonlinear dynamics of cylindrically and spherically expanding detonation waves. Journal of Fluid Mechanics, 522. pp. 329-356. ISSN 0022-1120

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Abstract

The nonlinear stability of cylindrically and spherically expanding detonation waves is investigated using numerical simulations for both directly (blast) initiated detonations and cases where the simulations are initialized by placing quasi-steady solutions corresponding to different initial shock radii onto the grid. First, high-resolution one-dimensional (axially or radially symmetric) simulations of pulsating detonations are performed. Emphasis is on comparing with the predictions of a recent one-dimensional linear stability analysis of weakly curved detonation waves. The simulations show that, in agreement with the linear analysis, increasing curvature has a rapid destabilizing effect on detonation waves. The initial size and growth rate of the pulsation amplitude decreases as the radius where the detonation first forms increases. The pulsations may reach a saturated nonlinear behaviour as the amplitude grows, such that the subsequent evolution is independent of the initial conditions. As the wave expands outwards towards higher (and hence more stable) radii, the nature of the saturated nonlinear dynamics evolves to that of more stable behaviour (e.g. the amplitude of the saturated nonlinear oscillation decreases, or for sufficiently unstable cases, the oscillations evolve from multi-mode to period-doubled to limit-cycle-type behaviour). For parameter regimes where the planar detonation is stable, the linear stability prediction of the neutrally stable curvature gives a good prediction of the location of the maximum amplitude (provided the stability boundary is reached before the oscillations saturate) and of the critical radius of formation above which no oscillations are seen. The linear analysis also predicts very well the dependence of the period on the radius, even in the saturated nonlinear regimes. Secondly, preliminary two-dimensional numerical simulations of expanding cellular detonations are performed, but it is shown that resolved and accurate calculations of the cellular dynamics are currently computationally prohibitive, even with a dynamically adaptive numerical scheme.

Item Type: Article
Copyright, Publisher and Additional Information: Copyright © 2005 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: Mrs Fiona Slade
Date Deposited: 05 Mar 2009 12:05
Last Modified: 17 Sep 2014 02:49
Published Version: http://dx.doi.org/10.1017/S0022112004001946
Status: Published
Publisher: Cambridge University Press
Refereed: Yes
Identification Number: 10.1017/S0022112004001946
URI: http://eprints.whiterose.ac.uk/id/eprint/7930

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