Dynamics of Hot-Spot Evolution in a Reactive, Compressible Flow

  • A. K. Kapila
  • T. L. Jackson
Part of the The IMA Volumes in Mathematics and Its Applications book series (IMA, volume 12)


A hot spot is a small region within an explosive bulk at which chemical activity occurs preferentially, in advance of its surroundings, when the system is ignited. Chemical reactions within the hot spot accelerate rapidly to provoke a localized explosion from which a combustion wave can propagate outwards. If the explosive is suitably preconditioned, the localized explosion may be strong enough to initiate a detonation. This study describes the dynamics of such a process, up to the instant just prior to the appearance of a reaction-induced blast wave at the edge of the hot spot. The birth of the blast wave is preceeded, in sequence, by a localized thermal runaway, the growth of a rapidly shrinking core of intense reaction at the runaway site, and the expansion of this core (without diminution of density) into a spatially homogeneous kernel of hot, pressurized, burnt material. The analysis combines asymptotics with numerics, and is based on a one-step Arrhenius model of the combustion process.


Boundary Layer Outer Region Blast Wave Logarithmic Singularity Explosion Phase 
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Copyright information

© Springer-Verlag New York Inc. 1988

Authors and Affiliations

  • A. K. Kapila
    • 1
  • T. L. Jackson
    • 2
  1. 1.Department of Mathematical SciencesRensselaer Polytechnic InstituteTroyUSA
  2. 2.Department of Mathematical SciencesOld Dominian UniversityNorfolkUSA

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