Detonation stability in the chain-branching regime assuming a small initiation rate
Date
2012
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
Abstract
Hydrogen chemistry is characterized by a specific chain-branching chemical kinetic mechanism leading to an S-shaped chain-branching explosion diagram, and characterized by an induction length much longer than the main reaction zone controlled by chain-branching. A simple three step kinetic scheme helps understanding how chain-branching works, and how it may affect detonation stability. A stability analysis of the steady, one dimensional Zel'dovich-von Neumann-Doering (ZND) detonation wave is performed for the case where the post-shock state lies inside the chain-branching explosion region, assuming that the initiation rate is small, which is especially accurate in the case of hydrogen. Instability of the planar wave is thought to be related to the cellular structure adopted by 11 early all detonation waves observed in experiments. Linear stability entails identifying whether the growth rate of a small perturbation is positive. The perturbation problem depends upon the steady, planar ZND reference solution, the stability of which is being investigated. Thus the coefficients in the linear perturbation problem depend upon the longitudinal coordinate, but not upon time nor the transverse coordinate. Hence the solution can be expressed in Fourier space in time and in relation to the transverse coordinate. Because the ZND solution is obtained numerically, the perturbation problem also requires a numerical solution. In relation to previous stability analysis, the main challenge in the current study was in formulating the proper boundary conditions, under the assumption of slow initiation rate. Results consist of the growth rates and frequencies of the dominant eigenmodes. Although the formulation handles transverse modes with no additional difficulty, results shown only consider longitudinal modes.
Description
Bibliography: p. 97-107
Keywords
Citation
Lopez-Aoyagi, M. M. (2012). Detonation stability in the chain-branching regime assuming a small initiation rate (Master's thesis, University of Calgary, Calgary, Canada). Retrieved from https://prism.ucalgary.ca. doi:10.11575/PRISM/4560