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A Zel’dovich–von Neumann–Döring-like detonation wave in a multi-temperature mixture

Published online by Cambridge University Press:  02 May 2019

Damir Madjarević Open the ORCID record for Damir Madjarević [Opens in a new window] ,
Srboljub Simić Open the ORCID record for Srboljub Simić [Opens in a new window]  and
Ana Jacinta Soares Open the ORCID record for Ana Jacinta Soares [Opens in a new window]
Damir Madjarević*
Affiliation:
Department of Mechanics, Faculty of Technical Sciences, University of Novi Sad, 21101 Novi Sad, Serbia
Srboljub Simić
Affiliation:
Department of Mathematics and Informatics, Faculty of Sciences, University of Novi Sad, 21101 Novi Sad, Serbia
Ana Jacinta Soares
Affiliation:
Centro de Matemática, Universidade do Minho, 4710-057 Braga, Portugal
*
†Email address for correspondence: damirm@uns.ac.rs
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Abstract

The detonation wave structure is analysed in a binary mixture undergoing a reversible chemical reaction represented by $A_{r}\rightleftharpoons A_{p}$. It is assumed that the flow satisfies the proper basic assumptions of the Zel’dovich–von Neumann–Döring (ZND) detonation model, namely the flow is one-dimensional and the shock is represented by a jump discontinuity, but the assumption of local thermodynamic equilibrium is disregarded. This allows us to deeply investigate the coupling between the detonation structure of overdriven detonations and its chemical kinetics. The thermodynamic non-equilibrium effects are taken into account in the mathematical description, using the model of a multi-temperature mixture developed within extended thermodynamics, which has been proved to be consistent with a kinetic theory approach. The reaction rate is then enriched with terms that take into account the temperatures of the constituents. The results show that the temperature difference between components within the detonation wave structure, which describes thermodynamic non-equilibrium, is driven by the chemical reaction. Numerical computations confirm the existence of non-monotonic profiles in the reaction zone of overdriven detonations which are sensitive to changes in the activation energy and reaction heat.

JFM classification

Reacting Flows: Detonations Compressible Flows: Gas dynamics Rarefied Gas Flow: Kinetic theory
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 869 , 25 June 2019 , pp. 674 - 705
Copyright
© 2019 Cambridge University Press 

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