Instabilities and Nonlinear Patterns of Overdriven Detonations in Gases

Abstract

Linear and weakly nonlinear analyses in the neighborhood of the multidimensional instability threshold of overdriven detonations propagating in gases are presented. An asymptotic solution to the reactive Euler equations is obtained in a “Newtonian limit” yielding a nonlinear integral-differential equation for the dynamics of the cellular front. The solution is valid for a general irreversible kinetics of the chemical heat release but is limited to strongly overdriven regimes. Mach-stems formation is described by a Burgers type equation. “Diamond” patterns similar to those observed in experiments are solutions to this equation. A nonlinear selection mechanism of the pattern is described, participating to the explanation of a mean cell size much larger than the unperturbed detonation thickness. An unusual self-sustained mean streaming motion is also exhibited in the nonlinear analysis. A particular attention is paid to the physical insights into this difficult hyperbolic and nonlinear problem whose asymptotic solution has been obtained very recently.

This article has been written for the proceedings of summer schools at Cargèse and Peyresc in France. It is based on a compilation of a series of recent articles by the author and collaborators, R. Daou, B. Denet, L. He and F.A. Willliams.