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The role of multidimensional instabilities in direct initiation of gaseous detonations in free space

Published online by Cambridge University Press:  20 January 2017

Hua Shen  and
Matteo Parsani
Hua Shen*
Affiliation:
King Abdullah University of Science and Technology (KAUST), Extreme Computing Research Center (ECRC), Computer, Electrical and Mathematical Sciences & Engineering (CEMSE), Thuwal, 23955-6900, Kingdom of Saudi Arabia
Matteo Parsani
Affiliation:
King Abdullah University of Science and Technology (KAUST), Extreme Computing Research Center (ECRC), Computer, Electrical and Mathematical Sciences & Engineering (CEMSE), Thuwal, 23955-6900, Kingdom of Saudi Arabia
*
†Email address for correspondence: hua.shen@kaust.edu.sa
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Abstract

We numerically investigate the direct initiation of detonations driven by the propagation of a blast wave into a unconfined gaseous combustible mixture to study the role played by multidimensional instabilities in direct initiation of stable and unstable detonations. To this end, we first model the dynamics of unsteady propagation of detonation using the one-dimensional compressible Euler equations with a one-step chemical reaction model and cylindrical geometrical source terms. Subsequently, we use two-dimensional compressible Euler equations with just the chemical reaction source term to directly model cylindrical detonations. The one-dimensional results suggest that there are three regimes in the direct initiation for stable detonations, that the critical energy for mildly unstable detonations is not unique, and that highly unstable detonations are not self-sustainable. These phenomena agree well with one-dimensional theories and computations available in the literature. However, our two-dimensional results indicate that one-dimensional approaches are valid only for stable detonations. In mildly and highly unstable detonations, one-dimensional approaches break down because they cannot take the effects and interactions of multidimensional instabilities into account. In fact, instabilities generated in multidimensional settings yield the formation of strong transverse waves that, on one hand, increase the risk of failure of the detonation and, on the other hand, lead to the initiation of local over-driven detonations that enhance the overall self-sustainability of the global process. The competition between these two possible outcomes plays an important role in the direct initiation of detonations.

JFM classification

Reacting Flows: Detonations Reacting Flows: Reacting Flows Compressible Flows: Shock waves

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Type
Rapids
Information
Journal of Fluid Mechanics , Volume 813 , 25 February 2017 , R4
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Copyright
© 2017 Cambridge University Press 

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