Comptes Rendus
no. 4
Patterns and dynamics: homage to Pierre Coullet / Formes et dynamique : hommage à Pierre Coullet
Advances in the analytical study of the dynamics of gaseous detonation waves
Paul Clavin1
1 Aix–Marseille Université, CNRS, Centrale Marseille, IRPHE UMR7342, 49, rue Frédéric-Joliot-Curie, 13384 Marseille, France
Comptes Rendus. Mécanique, Volume 347 (2019) no. 4, pp. 273-286.

Recent theoretical results on the dynamics of gaseous detonations are presented. An asymptotic analysis is performed, retaining the physical mechanisms controlling the modifications to the inner structure of the detonation. As a result, the system of hyperbolic equations for the compressible fluid mechanics coupled with a detailed chemical kinetics of heat release is reduced to a single integral equation for the propagation velocity of the combustion wave versus time. Concerning the direct initiation of spherical detonations by a blast wave, curvature effects are shown to be responsible for a critical condition of initiation. Near criticality, the role of the unsteadiness of the inner structure is pointed out. The whole complexity of the critical dynamics is reproduced and explained by the integral equation. The necessary background knowledge in gaseous detonation is recalled in the two first sections of the article in order to facilitate the reading by non-specialists.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crme.2019.03.008
Mots clés : Nonlinear hyperbolic equations, Asymptotic analysis, Integral equation
Paul Clavin 1

1 Aix–Marseille Université, CNRS, Centrale Marseille, IRPHE UMR7342, 49, rue Frédéric-Joliot-Curie, 13384 Marseille, France 
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Paul Clavin. Advances in the analytical study of the dynamics of gaseous detonation waves. Comptes Rendus. Mécanique, Volume 347 (2019) no. 4, pp. 273-286. doi : 10.1016/j.crme.2019.03.008. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2019.03.008/

[1] P. Clavin Nonlinear dynamics of shocks and detonation waves in gases, Combust. Sci. Technol., Volume 189 (2017), pp. 747-775

[2] P. Clavin; G. Searby Combustion Waves and Fronts in Flows, Cambridge University Press, 2016

[3] P. Clavin; B. Denet Decay of plane detonation waves to the self-propagating Chapman–Jouguet regime, J. Fluid Mech., Volume 845 (2018), pp. 170-202

[4] P. Clavin; B. Denet Asymptotic analysis of direct initiation of gaseous detonation, J. Fluid Mech. (2019) (submitted for publication)

[5] L. He; P. Clavin On the direct initiation of gaseous detonations by an energy source, J. Fluid Mech., Volume 277 (1994), pp. 227-248

[6] L. He Theoretical determination of the critical conditions for the direct initiation of detonation in hydrogen-oxygen mixtures, Combust. Flame, Volume 104 (1996), pp. 401-418

[7] C.A. Eckert; J.J. Quirk; J.E. Shepherd The role of unsteadiness in direct initiation of gaseous detonation, J. Fluid Mech., Volume 421 (2000), pp. 147-183

[8] P. Clavin; F.A. Williams Dynamics of planar gaseous detonations near Chapman–Jouguet conditions for small heat release, Combust. Theory Model., Volume 6 (2002), pp. 127-139

[9] P. Clavin; F.A. Williams Multidimensional stability analysis of gaseous detonations near Chapman–Jouguet conditions for small heat release, J. Fluid Mech., Volume 624 (2009), pp. 125-150

[10] P. Clavin; L. He Stability and nonlinear dynamics of one-dimensional overdriven detonations in gases, J. Fluid Mech., Volume 306 (1996), pp. 353-378

[11] A. Liñan; V. Kurdyumov; A. Sanchez Initiation of reacting blast waves by external energy sources, C. R. Mecanique, Volume 340 (2012), pp. 829-844

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