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The effect of diffusion on the dynamics of unsteady detonations

Published online by Cambridge University Press:  17 April 2012

C. M. Romick ,
T. D. Aslam  and
J. M. Powers
C. M. Romick
Affiliation:
Department of Aerospace and Mechanical Engineering, University of Notre Dame, Notre Dame, IN 46556, USA
T. D. Aslam
Affiliation:
Weapons Experiments Division, Los Alamos National Laboratory, Los Alamos, NM 87545, USA
J. M. Powers*
Affiliation:
Department of Aerospace and Mechanical Engineering, University of Notre Dame, Notre Dame, IN 46556, USA
*
†Email address for correspondence: powers@nd.edu
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Abstract

The dynamics of a one-dimensional detonation predicted by a one-step irreversible Arrhenius kinetic model are investigated in the presence of mass, momentum and energy diffusion. A study is performed in which the activation energy is varied and the length scales of diffusion and reaction are held constant. As the activation energy is increased, the system goes through a series of period-doubling events and eventually undergoes a transition to chaos. The rate at which these bifurcation points converge is calculated and shown to be in agreement with the Feigenbaum constant. Within the chaotic regime, there exist regions in which there are limit cycles consisting of a small number of oscillatory modes. When an appropriately fine grid is used to capture mass, momentum and energy diffusion, predictions are independent of the differencing scheme. Diffusion affects the behaviour of the system by delaying the onset of instability and strongly influencing the dynamics in the unstable regime. The use of the reactive Euler equations to predict detonation dynamics in the unstable and marginally stable regimes is called into question as the selected reactive and diffusive length scales are representative of real physical systems; reactive Navier–Stokes is a more appropriate model in such regimes.

JFM classification

Nonlinear Dynamical Systems: Bifurcation Reacting Flows: Detonations Reacting Flows: Reacting Flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 699 , 25 May 2012 , pp. 453 - 464
Copyright
Copyright © Cambridge University Press 2012

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