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Stability of detonations for an idealized condensed-phase model

Published online by Cambridge University Press:  08 January 2008

M. SHORT ,
I. I. ANGUELOVA ,
T. D. ASLAM ,
J. B. BDZIL ,
A. K. HENRICK  and
G. J. SHARPE
M. SHORT
Affiliation:
Theoretical and Applied Mechanics, University of Illinois, Urbana, IL 61801, USA
I. I. ANGUELOVA
Affiliation:
Department of Mathematics, University of Illinois, Urbana, IL 61801, USA
T. D. ASLAM
Affiliation:
Los Alamos National Laboratory, Los Alamos, NM 87545, USA
J. B. BDZIL
Affiliation:
Los Alamos National Laboratory, Los Alamos, NM 87545, USA
A. K. HENRICK
Affiliation:
Los Alamos National Laboratory, Los Alamos, NM 87545, USA Department of Aerospace and Mechanical Engineering, University of Notre Dame, Notre Dame, IN 46556, USA
G. J. SHARPE
Affiliation:
Los Alamos National Laboratory, Los Alamos, NM 87545, USA
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Abstract

The stability of travelling wave Chapman–Jouguet and moderately overdriven detonations of Zeldovich–von Neumann–Döring type is formulated for a general system that incorporates the idealized gas and condensed-phase (liquid or solid) detonation models. The general model consists of a two-component mixture with a one-step irreversible reaction between reactant and product. The reaction rate has both temperature and pressure sensitivities and has a variable reaction order. The idealized condensed-phase model assumes a pressure-sensitive reaction rate, a constant-γ caloric equation of state for an ideal fluid, with the isentropic derivative γ=3, and invokes the strong shock limit. A linear stability analysis of the steady, planar, ZND detonation wave for the general model is conducted using a normal-mode approach. An asymptotic analysis of the eigenmode structure at the end of the reaction zone is conducted, and spatial boundedness (closure) conditions formally derived, whose precise form depends on the magnitude of the detonation overdrive and reaction order. A scaling analysis of the transonic flow region for Chapman–Jouguet detonations is also studied to illustrate the validity of the linearization for Chapman–Jouguet detonations. Neutral stability boundaries are calculated for the idealized condensed-phase model for one- and two-dimensional perturbations. Comparisons of the growth rates and frequencies predicted by the normal-mode analysis for an unstable detonation are made with a numerical solution of the reactive Euler equations. The numerical calculations are conducted using a new, high-order algorithm that employs a shock-fitting strategy, an approach that has significant advantages over standard shock-capturing methods for calculating unstable detonations. For the idealized condensed-phase model, nonlinear numerical solutions are also obtained to study the long-time behaviour of one- and two-dimensional unstable Chapman–Jouguet ZND waves.

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Papers
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Journal of Fluid Mechanics , Volume 595 , 25 January 2008 , pp. 45 - 82
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Copyright © Cambridge University Press 2008

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References

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