Hostname: page-component-848d4c4894-r5zm4 Total loading time: 0 Render date: 2024-06-25T15:25:36.700Z Has data issue: false hasContentIssue false
  • English
  • Français

Asymptotic analysis of the critical dynamics of spherical gaseous detonations

Published online by Cambridge University Press:  29 March 2021

Paul Clavin Open the ORCID record for Paul Clavin [Opens in a new window] ,
Raúl Hernández Sánchez Open the ORCID record for Raúl Hernández Sánchez [Opens in a new window]  and
Bruno Denet Open the ORCID record for Bruno Denet [Opens in a new window]
Paul Clavin*
Affiliation:
Aix Marseille Université, CNRS, Centrale Marseille, IRPHE UMR7342, 49 Rue F. Joliot Curie, 13384Marseille, France
Raúl Hernández Sánchez
Affiliation:
Aix Marseille Université, CNRS, Centrale Marseille, IRPHE UMR7342, 49 Rue F. Joliot Curie, 13384Marseille, France
Bruno Denet
Affiliation:
Aix Marseille Université, CNRS, Centrale Marseille, IRPHE UMR7342, 49 Rue F. Joliot Curie, 13384Marseille, France
*
†Email address for correspondence: paul.clavin@wanadoo.fr
Get access Rights & Permissions [Opens in a new window]

Abstract

The critical dynamics of supersonic combustion waves is studied in the context of the direct initiation of detonation in a spherical geometry. The study is performed by an asymptotic analysis in the limit of small heat release, including unsteadiness, curvature and the gradient of the burnt-gas flow. Derivation of analytical expressions for the rarefaction wave in the burnt-gas flow, combined with numerical studies, provides the basis of the analysis. The critical trajectories ‘detonation velocity vs front radius’ $\mathcal {D}(r_f)$ are characterized by a decay well below the Chapman–Jouguet (CJ) velocity at a small radius (however, larger than the detonation thickness), followed by a re-acceleration process back to a CJ detonation. The phenomenon is explained by the dynamics of the sonic point inside the inert rarefaction wave behind the reaction zone. The key mechanism is a critical slowdown as soon as the sonic condition (relative to the lead shock) approaches the reaction zone from behind, leading to an increase of the time delay in the nonlinear response of the combustion wave to the rarefaction-wave-induced decay. Detonation fails if the rate of decay is strong enough to prevent the sonic point catching the reaction zone. Concerning successful initiation, the link between the trajectories $\mathcal {D}(r_f)$ of the fully unsteady problem and of the self-similar CJ solution of the discontinuous model is deciphered in the long-time limit.

JFM classification

Compressible Flows: Detonation waves Reacting Flows: Combustion Compressible Flows: Gas dynamics
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 915 , 25 May 2021 , A122
Check for updates
Copyright
© The Author(s), 2021. Published by Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Clavin, P. & Denet, B. 2018 Decay of plane detonation waves to the self-propagating Chapman–Jouguet regime. J. Fluid Mech. 845, 170–202.CrossRefGoogle Scholar
Clavin, P. & Denet, B. 2020 Analytical study of the direct initiation of gaseous detonations for small heat release. J. Fluid Mech. 897, A30.CrossRefGoogle Scholar
Clavin, P. & Searby, G. 2016 Combustion Waves and Fronts in Flows. Cambridge University Press.CrossRefGoogle Scholar
Clavin, P. & Williams, F.A. 2002 Dynamics of planar gaseous detonations near Chapman–Jouguet conditions for small heat release. Combust. Theor. Model. 6, 127–129.CrossRefGoogle Scholar
Eckett, C.A., Quirk, J.J. & Shepherd, J.E. 2000 The role of unsteadiness in direct initiation of gaseous detonations. J. Fluid Mech. 421, 147–183.CrossRefGoogle Scholar
He, L. 1996 Theoretical determination of the critical conditions for the direct initiation of detonations in hydrogen–oxygen mixtures. Combust. Flame 104, 401–418.CrossRefGoogle Scholar
He, L. & Clavin, P. 1994 On the direct initiation of gaseous detonations by an energy source. J. Fluid Mech. 277, 227–248.CrossRefGoogle Scholar
Li nan, A., Kurdyumov, V. & Sanchez, A.L. 2012 Initiation of reactive blast waves by external energy source. C. R. Méc. 340, 829–844.CrossRefGoogle Scholar
Ng, H. & Lee, J.H.S. 2003 Direct initiation of detonation with a multi-step reaction scheme. J. Fluid Mech. 476, 179–211.CrossRefGoogle Scholar
Sanchez, A.L. & Williams, F.A. 2014 Recent advances in understanding of flammability characteristics of hydrogen. Prog. Energy Combust. Sci. 41, 1–55.CrossRefGoogle Scholar
Sedov, L.I. 1946 Propagation of strong blast waves. Prikl. Mat. Meckh. 10, 241–250.Google Scholar
Taylor, G.I. 1950 a The dynamics of combustion products behind plane and spherical detonation fronts. Proc. R. Soc. Lond. A 200, 235–247.Google Scholar
Taylor, G.I. 1950 b The formation of a blast wave by a very intense explosion. Proc. R. Soc. Lond. A 201, 159–174.Google Scholar
Zeldovich, Y.B. 1942 On the distribution of pressure and velocity in products of detonation blasts, in particular for spherical propagating detonation waves. Zh. Eksp. Teor. Fiz. 12, 389–406.Google Scholar