On the characteristics of two-dimensional double cellular detonations with two successive reactions model

Double cellular detonations were numerically investigated using two-dimensional Euler equations with two successive chemical reactions, whose reaction lengths differ one order of magnitude. Simulated soot track images showed the double cellular structure with two cell widths that differ one order of magnitude, as well as previous experiments and numerical simulations. We successfully divided the double cellular detonation with two successive exothermic reactions into two detonations, primary and secondary detonations, with a single exothermic reaction, based on p-v relation of Rayleigh line and Hugoniot curves with the addition of the hypothetical condition of intermediate initial state. The ratio of cell widths of primary and secondary detonations showed good agreement with that caused by the first and second reactions of double cellular detonation, and there was no interaction between two successive chemical reactions. The linear stability analysis of planar detonation and the soot rack images of double, primary and secondary detonations showed that instabilities of primary and secondary detonations are dominant to that of double cellular detonation with two successive reactions. We confirmed the validity of division of two successive reactions to clarify the detonation instability and its cellular structure.