Non-dimensionalized distances and limits for the transition of deflagration to detonation

This experimental work investigates the possibility to non-dimensionalize the limits and the distances of the deflagration-to-detonation transition process (DDT). The deflagration was ignited using jets of hot gases generated by the impact of a Chapman–Jouguet detonation on a multi-perforated plate. The tube was 1 m long with a square cross section 40 × 40 mm 2 . The reactive mixtures were the stoichiometric compositions of hydrogen, methane, and oxygen ( 1 - x ) H 2 + x CH 4 + 1 / 2 ( 1 + 3 x ) O 2 with the composition parameter x ranging from 0 to 1. The initial pressure p 0 was varied from 12 to 35 kPa, and the initial temperature was 294 K. The widths of the detonation cells and the conditions and distances for DDT were obtained as functions of x , p 0 , the thickness of the plate, and the number and diameter of its perforations. The cell width was used as the reference length. The non-dimensional DDT distances correlate well with the non-dimensional number representing the surface re-ignition effect in the form of a concave increasing function. The non-dimensional DDT limits appear to be independent of the surface dissipation phenomena in the perforations. These trends are found to be independent of the regularity of the detonation cells. DDT processes are very dependent on the system configuration and the ignition conditions, but our analysis suggests that the proper selection of non-dimensional numbers based on the system characteristics can predict the DDT limits and distances to a reasonable approximation.