  The present study addresses the reaction zone structure and burning mechanism
of unstable detonations. Experiments investigated mainly two-dimensional
methane-oxygen cellular detonations in a thin channel geometry. The
sufficiently high temporal resolution permitted to determine the PDF of the
shock distribution, a power-law with an exponent of -3, and the burning rate of
unreacted pockets from their edges - through surface turbulent flames with a
speed approximately 3-7 times larger than the laminar one at the local
conditions. Numerical simulations were performed using a novel Large Eddy
Simulation method where the reactions due to both auto-ignition and turbulent
transport and treated exactly at the sub-grid scale in a reaction-diffusion
formulation. The model is an extension of Kerstein & Menon's Linear Eddy Model
for Large Eddy Simulation to treat flows with shock waves and rapid gasdynamic
transients. The two-dimensional simulations recovered well the amplification of
the laminar flame speed owing to the turbulence generated mainly by the shear
layers originating from the triple points and subsequent Richtmyer-Meshkov
instability associated with the internal pressure waves. The simulations
clarified how the level of turbulence generated controlled the burning rate of
the pockets, the hydrodynamic thickness of the wave, the cellular structure and
its distribution. Three-dimensional simulations were found in general good
agreement with the two-dimensional ones, in that the sub-grid scale model
captured the ensuing turbulent burning once the scales associated with the
cellular dynamics, where turbulent kinetic energy is injected, are well
resolved.
