Geometric modeling and analysis of detonation cellular stability

A geometric model with a low computational complexity capable of simulating detonation behavior in physical systems is proposed. In support of the geometric model development, a series of cylindrical 1D simulations with a variable size initiation kernel are performed in hydrogen-oxygen mixtures. From these 1D simulations a detonation cell stabilization mechanism is identified. The stabilization mechanism is predicated on the size of the gap between the pressure and temperature fronts at the point where the average pressure front velocity along one cell length is equal to the CJ velocity. This gap, in a multidimensional detonation, is the ignition kernel of a subsequent blast, and dictates the formation of the subsequent cell. Serial analysis of blasts in this context leads to a unique stable blast kernel size for any mixture, which, within the uncertainty of the initial kernel state, can predict the experimental cell length for mixtures considered in this study. Using a tabulation of the 1D simulations as an input, a formulation and sample results of the geometric model are shown. The geometric model can reproduce both qualitative and quantitative features of experimental detonation cellular structure.