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Communication Dans Un Congrès Année : 2003

Instabilities and nonlinear diamond patterns of detonations in gases

Résumé

The spatio-temporal structure of gaseous detonations have been studied experimentally since the 1950s. They differ notably from the dissipative structures of other non-equilibrium systems such as flames, growing crystals, Rayleigh-Bernard convection etc. A detonation is a supersonic combustion wave consisting of a strong inert schock followed by a reacting flow. The molecular transports are localized inside the leading shock (which may be considered a hydrodynamic dicontinuity) and may be neglected in the compressed gases which are governed by the Euler reactive equation. The dynamics and structure of the detonation wave are thus solutions of a nonlinear hyperbolic problem. One of the striking observations in experiments is the formation of Mach-stems with triple point configurations travelling to the front at nearly the sound speed in the burned gas. Their trajectories have a diamond pattern with cell sizes two orders of magnitude larger than the unperturbed detonation thickness. The cell sizes, as recorded on soot-coated foils at the walls are used in an empirical way for many applied purposes such as for nuclear reactor safety. The role of detonation celluar structure in astrophysics has animpact on the observed spectra of type 1a supernovae. A challenging problem is to relate the pattern to the properties of the reactive mixture. Physical insights are elusive and there is no convincing explanation of neither the size for the shape of the pattern. In order to provide and overall physical understanding, our approachis to carry out a nonlinear study in the neighbourhood of the instability threshhold. Even limited to weakly unstable detonation waves, the analysis is still too complex to be carried out without further approximations. Our method consists in finding an asymptotic solution in the double limit of a large propagation Mach number andof a small difference between specific heats C_p and C_v. Such alimit was already used a long time ago, in hypersonic flow theory around the 1950s, and is known as "Newtonian flow theory"reference to Newton's contribution to the science of ballistics published in "Principia". Our final result is a nonlinear integral-differentiale quation for the front dynamics describing time dependetn patterns qualitatively similar to those observed in experiments. An unusual front dynamics involving a self-sustained mean streaming motion isobserved. Formation of cusps representative of Mach-stems andpattern selection are described explaining the large size of the cells. The analysis is valid for a general chemical kintetics of an irreversible exothermal reaction but is limited to overdriven regimes..
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Dates et versions

hal-00086341 , version 1 (18-07-2006)

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  • HAL Id : hal-00086341 , version 1

Citer

Paul Clavin. Instabilities and nonlinear diamond patterns of detonations in gases. British Applied Mathematics Colloquium, BAMC'03, 2003, Southampton, United Kingdom. ⟨hal-00086341⟩
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