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Mean structure of one-dimensional unstable detonations with friction

Published online by Cambridge University Press:  06 March 2014

Aliou Sow ,
Ashwin Chinnayya  and
Abdellah Hadjadj
Aliou Sow
Affiliation:
CORIA-UMR 6614, Normandie University, CNRS-University & INSA of Rouen, 76800 Saint-Etienne du Rouvray, France
Ashwin Chinnayya
Affiliation:
CORIA-UMR 6614, Normandie University, CNRS-University & INSA of Rouen, 76800 Saint-Etienne du Rouvray, France Institut PPrime, CNRS UPR 3346, ENSMA & University of Poitiers, 86961 Futuroscope-Chasseneuil, France
Abdellah Hadjadj*
Affiliation:
CORIA-UMR 6614, Normandie University, CNRS-University & INSA of Rouen, 76800 Saint-Etienne du Rouvray, France
*
†Email address for correspondence: hadjadj@coria.fr
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Abstract

This investigation deals with the study of the mean structure of a mildly unstable non-ideal detonation wave. The analysis is based on the integration of one-dimensional reactive Euler equations with friction forces using a third-order Runge–Kutta scheme and a fifth-order weighted essentially non-oscillatory (WENO5) spatial discretization. A one-step Arrhenius reaction mechanism is used for modelling the chemical reaction. When the frictional forces are active, the limit cycle based on the post-shock pressure reveals an enhanced pulsating behaviour of the downstream subsonic reaction zone compared to the ideal case. The results show that the detonation-velocity deficit increases as the mean reaction zone becomes thicker compared to the generalized ZND model. A new master equation, based on the Favre-averaged quantities, is derived and analysed along with new sonicity and thermicity conditions. The analysis of the species, momentum and energy balances reveals that the presence of mechanical fluctuations within the reaction zone constitutes another source of energy withdrawal, meaning that the detonation deviates from its laminar structure. Furthermore, the compressibility of the flow is analysed and the relationships between the fluctuations of temperature, velocity and reactive scalar are discussed in terms of strong Reynolds analogies.

JFM classification

Compressible Flows: Compressible Flows Reacting Flows: Detonations
Type
Papers
Information
Journal of Fluid Mechanics , Volume 743 , 25 March 2014 , pp. 503 - 533
Copyright
© 2014 Cambridge University Press 

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