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Propagation of gaseous detonation waves in a spatially inhomogeneous reactive medium

XiaoCheng Mi and Andrew J. Higgins*

Hoi Dick Ng and Charles B. Kiyanda

Nikolaos Nikiforakis

  • Department of Mechanical Engineering, McGill University, Montreal, Quebec, Canada H3A 0C3

  • Department of Mechanical and Industrial Engineering, Concordia University, Montreal, Quebec, Canada H4B 1R6

  • Cavendish Laboratory, Department of Physics, University of Cambridge, Cambridge CB3 0HE, United Kingdom

  • *Corresponding author: andrew.higgins@mcgill.ca
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Phys. Rev. Fluids 2, 053201 – Published 31 May, 2017

DOI: https://doi.org/10.1103/PhysRevFluids.2.053201

Abstract

Detonation propagation in a compressible medium wherein the energy release has been made spatially inhomogeneous is examined via numerical simulation. The inhomogeneity is introduced via step functions in the reaction progress variable, with the local value of energy release correspondingly increased so as to maintain the same average energy density in the medium and thus a constant Chapman-Jouguet (CJ) detonation velocity. A one-step Arrhenius rate governs the rate of energy release in the reactive zones. The resulting dynamics of a detonation propagating in such systems with one-dimensional layers and two-dimensional squares are simulated using a Godunov-type finite-volume scheme. The resulting wave dynamics are analyzed by computing the average wave velocity and one-dimensional averaged wave structure. In the case of sufficiently inhomogeneous media wherein the spacing between reactive zones is greater than the inherent reaction zone length, average wave speeds significantly greater than the corresponding CJ speed of the homogenized medium are obtained. If the shock transit time between reactive zones is less than the reaction time scale, then the classical CJ detonation velocity is recovered. The spatiotemporal averaged structure of the waves in these systems is analyzed via a Favre-averaging technique, with terms associated with the thermal and mechanical fluctuations being explicitly computed. The analysis of the averaged wave structure identifies the super-CJ detonations as weak detonations owing to the existence of mechanical nonequilibrium at the effective sonic point embedded within the wave structure. The correspondence of the super-CJ behavior identified in this study with real detonation phenomena that may be observed in experiments is discussed.

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Outline

Information

Phys. Rev. Fluids 2, 053201– Published 31 May, 2017
  • Received 8 December 2016
  • Revised 3 March 2017

©2017 American Physical Society

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