Mathematical Problems in Engineering
Volume 5 (1999), Issue 3, Pages 223-254

Asymptotic analysis of the structure of a steady planar detonation: Review and extension

W. B. Bush and L. Krishnamurthy

Aerospace Engineering Program, Florida Institute of Technology, Melbourne 32901-6975, FL, USA

Received 9 April 1999

Copyright © 1999 W. B. Bush and L. Krishnamurthy. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The structure of a steady planar Chapman–Jouguet detonation, which is supported by a direct first-order one-step irreversible exothermic unimolecular reaction, subject to Arrhenius kinetics, is examined. Solutions are studied, by means of a limit-process-expansion analysis, valid for Λ, proportional to the ratio of the reaction rate to the flow rate, going to zero, and for β, proportional to the ratio of the activation temperature to the maximum flow temperature, going to infinity, with the product Λβ1/2 going to zero. The results, essentially in agreement with the Zeldovich–von Neumann–Doring model, show that the detonation consists of (1) a three-region upstream shock-like zone, wherein convection and diffusion dominate; (2) an exponentially thicker five-region downstream deflagration-like zone, wherein convection and reaction dominate; and (3) a transition zone, intermediate to the upstream and downstream zones, wherein convection, diffusion, and reaction are of the same order of magnitude. It is in this transition zone that the ideal Neumann state is most closely approached.