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Title:Asymptotic theory of ignition and failure of self-sustained detonations
Author(s):Kasimov, Aslan R.; Stewart, D. Scott
Abstract:Based on a general theory of detonation waves with an embedded sonic locus that we have developed in Kasimov (2004) and Stewart & Kasimov (2004), we carry out asymptotic analysis of weakly-curved slowly-varying detonation waves and show that the theory predicts the phenomenon of detonation ignition and failure. The analysis is not restricted to near Chapman–Jouguet detonation speeds and is capable of predicting quasi-steady, normal detonation shock speed, curvature (D–k) curves with multiple turning points. An evolution equation that retains the shock acceleration, D(dot), namely a D(dot)–D–k relation is rationally derived and its solution for spherical (or cylindrical) detonation is shown to reproduce the ignition/failure phenomenon observed in both numerical simulations of blast wave initiation and in experiments. A simple physically transparent explanation of the ignition phenomenon is given in terms of the form of the evolution equation. A single-step chemical reaction described by one progress variable is employed, but the kinetics is sufficiently general and is not restricted to Arrhenius form, although most specific calculations in this work are performed for Arrhenius kinetics. As an example, we calculate critical energies of direct initiation for hydrogen–oxygen mixtures and find close agreement with available experimental data.
Issue Date:2004-02
Publisher:Department of Theoretical and Applied Mechanics (UIUC)
Series/Report:TAM Reports 1042
Genre:Technical Report
Article
Type:Text
Language:English
URI:http://hdl.handle.net/2142/238
ISSN:0073-5264
Publication Status:published or submitted for publication
Peer Reviewed:is peer reviewed
Rights Information:Copyright 2005 Cambridge University Press
Date Available in IDEALS:2007-03-08
Is Version Of:Published as: Aslan R. Kasimov and D. Scott Stewart. Asymptotic theory of ignition and failure of self-sustained detonations. Journal of Fluid Mechanics, v 525,2005, p 161-192. DOI: 10.1017/S0022112004002599. http://hdl.handle.net/2142/681.


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  • Technical Reports - Theoretical and Applied Mechanics (TAM)
    TAM technical reports include manuscripts intended for publication, theses judged to have general interest, notes prepared for short courses, symposia compiled from outstanding undergraduate projects, and reports prepared for research-sponsoring agencies.

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