Cell size and DDT scaling for ethylene–oxygen–nitrogen detonation

Detonation experiments were performed in ethylene–oxygen–nitrogen mixtures, varying both the equivalence ratio from 0.6–2.5 and the diluent from 0%–74% by volume. The experiments were performed at 1.00 bar in a tube of circular cross-section. The first half of the tube length contained obstacles to promote deflagration-to-detonation transition (DDT), while the second half was smooth. The reported results span previously uncharacterized nitrogen-diluted, off-stoichiometric regimes and include the detonation cell size, its standard deviation, and the DDT run-up distance and time. The number of dominant length scales present in each cell size distribution was found to correlate qualitatively to the location of the maximum heat release rate in one-dimensional thermochemical calculations. Analysis of this new experimental data in conjunction with prior measurements and thermochemical stability parameters yielded several new correlations. A power law was found to describe the relationship between DDT run-up distance and time across all tested equivalence ratios. An improved scaling was found describing the proportional relationship between the measured cell size and computed induction zone length for these mixtures. A similar relationship was able to describe the measured variation in cell size. The DDT run-up distance and time were also correlated with cell size. The combination of these relationships substantially reduces the number of experiments needed to characterize the experimental detonation properties of this mixture, and possibly other mixtures. Finally, the measured cellular irregularity, quantified by the cell size coefficient of variation, was found to scale with reduced activation energy similarly to prior observations of other mixtures. The developed correlations were used to provide insight into this relationship. Novelty and Significance Statement New measurements of detonation in ethylene–oxygen–nitrogen mixtures are reported in previously uncharacterized regimes that are relevant to detonation combustors and industrial applications. Analysis yielded several novel correlations that significantly reduce the number of experimental measurements needed to characterize the variation of detonation cell size and DDT run-up distance with initial conditions. These findings also quantify the dependence of cellular irregularity.