University of Illinois Urbana-Champaign

Multi-dimensional stability of weak heat release detonations

Short, Mark; Stewart, D. Scott

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https://hdl.handle.net/2142/112588

Description

Title
Multi-dimensional stability of weak heat release detonations
Author(s)
  • Short, Mark
  • Stewart, D. Scott
Issue Date
1998-06
Keyword(s)
Heat Release Detonations
Abstract
The stability of an overdriven planar detonation wave is examined for a one-step Arrhenius reaction model with an order one post-shock temperature-scaled activation energy θ in the limit of a small post-shock temperature-scaled heat release β. The ratio of specific heats, γ, is taken such that (γ-1) = 0(1). Under these assumptions, which cover a wide range of realistic physical situations, the steady detonation structure can be evaluated explicitly, with the reactant mass fraction described by an exponentially decaying function. The analytical representation of the steady structure allows a normal-mode description of the stability behaviour to be obtained via a two-term asymptotic expansion in β. The resulting dispersion relation predicts that for a finite overdrive f, the detonation is always stable to two-dimensional disturbances. For large overdrives, the identification of regimes of stability or instability is found to depend on a choice of distinguished limit between the heat release β and the detonation propagation Mach number D*. Regimes of instability are found to be characterised by the presence of a single unstable oscillatory mode over a finite range of wave numbers.
Publisher
Department of Theoretical and Applied Mechanics. College of Engineering. University of Illinois at Urbana-Champaign
Series/Report Name or Number
  • TAM R 882
  • 1998-6008
ISSN
0073-5264
Type of Resource
text
Language
eng
Permalink
http://hdl.handle.net/2142/112588
Sponsor(s)/Grant Number(s)
Air Force Office of Scientific Research CTS-9616219; Air Force Wright Labs NGT 2-52229
Copyright and License Information
Copyright 1998 Board of Trustees of the University of Illinois

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Technical Reports - Theoretical and Applied Mechanics (TAM) PRIMARY
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.