University of Illinois Urbana-Champaign

Low-frequency two-dimensional linear instability of plane detonation

Short, Mark; Stewart, D. Scott

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https://hdl.handle.net/2142/112520

Description

Title
Low-frequency two-dimensional linear instability of plane detonation
Author(s)
  • Short, Mark
  • Stewart, D. Scott
Issue Date
1996-03
Keyword(s)
  • Plane Detonation
  • Linear Instability
Abstract
An analytical dispersion relation describing the low-frequency two-dimensional linear stability of a plane detonation wave characterized by a one-step Arrhenius reaction is derived using a normal mode approach and a combination of high-activation energy and Newtonian limit asymptotics, where the ratio of specific heats γ→1. The analysis relies on an assumption of a large activation energy in the plane steady-state detonation wave and a characteristic linear disturbance wavelength which is larger than the fire zone thickness. Newtonian limit asymptotics are employed to obtain a complete analytical description of the disturbance behaviour in the induction zone of the detonation wave. The analytical dispersion relation that is derived retains a dependence on the activation energy and demonstrates an excellent agreement with numerical solutions of the full linear stability problem for low-frequency, one- and two-dimensional disturbances even when the activation energy is only moderate. Moreover, the dispersion relation retains vitally important characteristics of the full problem such as stability of the detonation wave for decreasing activation energies or increasing overdrives. In addition, through a new detailed analysis of the behaviour of perturbations near the fire front, the present analysis is found to be equally valid for detonation waves travelling at the Chapman-Jouguet velocity or for detonation waves which are overdriven. It is found that in contrast to the standard imposition of a radiation or piston condition on acoustic disturbances in the equilibrium zone for overdriven waves, a compatibility condition on the perturbation jump conditions across the fire zone must be satisified for detonation waves propagating at the Chapman-Jouguet detonation velocity. An insight into the physical mechanisms of the one- and two-dimensional linear instability is also determined, and is found to involve an intricate coupling between acoustic and entropy wave propagation within the detonation wave.
Publisher
Department of Theoretical and Applied Mechanics. College of Engineering. University of Illinois at Urbana-Champaign
Series/Report Name or Number
  • TAM R 820
  • 1996-6007
ISSN
0073-5264
Type of Resource
text
Language
eng
Permalink
http://hdl.handle.net/2142/112520
Sponsor(s)/Grant Number(s)
Air Force Office of Scientific Research 96/03; US Air Force Wright Labs 96/03; Los Alamos National Labs 96/03
Copyright and License Information
Copyright 1996 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.