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

• Main Authors: Bush W. B., Krishnamurthy L.
• Format: Article
• Language: English
• Published: Hindawi Limited 1999-01-01
• Series: Mathematical Problems in Engineering
• Subjects: Asymptotic analysis; Planar detonation; Uniformly valid solution
• Online Access: http://www.hindawi.net/access/get.aspx?journal=mpe&volume=5&pii=S1024123X99001076

<p>The structure of a steady planar Chapman&#8211;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 <math alttext="$Lambda $"> <mi>&Lambda;</mi> </math>, proportional to the ratio of the reaction rate to the flow rate, going to zero, and for <math alttext="$eta $"> <mi>&beta;</mi> </math>, proportional to the ratio of the activation temperature to the maximum flow temperature, going to infinity, with the product <math alttext="$Lambda eta ^{1/2} $"> <mrow> <mi>&Lambda;</mi> <msup> <mi>&beta;</mi> <mrow> <mn>1</mn> <mo>&sol;</mo> <mn>2</mn> </mrow> </msup> </mrow> </math> going to zero. The results, essentially in agreement with the Zeldovich&#8211;von Neumann&#8211;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.</p>