Formation and evolution of two-dimensional cellular detonations

This paper reports the results of numerical simulations of cellular detonations generated by using numerical noise as a source of initial fluctuations imposed on a strong planar shock propagating through the reactive medium. The calculations show that a plane detonation wave moving at Chapman-Jouguet (CJ) velocity is unstable to transverse perturbations with wavelength greater than one or two half-reaction-zone lengths. The numerical noise affects the initial cell formation process, but it has no influence on the cell size and regularity of the structures developed. Increasing the activation energy results in more irregular structures characterized by stronger triple points, larger variations of the local shock velocity inside the detonation cell, and higher frequency of appearance and disappearance of triple points. These features of the systems with irregular cellular structures can account for the experimental observation that such systems are less affected by boundary conditions. For the two-dimensional detonation, the average reaction zone is larger and maximum reaction rate is lower than in the one-dimensional case. This means that the formation of detonation cells reduces the maximum entropy production in the reaction zone, and slows down the approach of the system to the equilibrium state. This effect is shown to increase with activation energy due to larger unreacted gas pockets, and deeper penetration of the pockets into the region of mostly burned material.