Chapman-Jouguet deflagrations and their transition to detonation

We study experimentally fast flames and their transition to detonation in mixtures of methane, ethane, ethylene, acetylene, and propane mixtures with oxygen. Following the interaction of a detonation wave with a column of cylinders of varying blockage ratio, the experiments demonstrate that the fast flames established are Chapman-Jouguet deflagrations, in excellent agreement with the self-similar model of Radulescu et al. (2015). The experiments indicate that these Chapman-Jouguet deflagrations dynamically restructure and amplify into fewer stronger modes until the eventual transition to detonation. The transition length to a self-sustained detonation was found to correlate very well with the mixtures' sensitivity to temperature fluctuations, reflected by the $\chi$ parameter introduced by Radulescu, which is the product of the non-dimensional activation energy $E_a/RT$ and the ratio of chemical induction to reaction time $t_i/t_r$. Correlation of the measured DDT lengths determined that the relevant characteristic time scale from chemical kinetics controlling DDT is the energy release or excitation time $t_r$. Correlations with the cell size also capture the dependence of the DDT length on $\chi$ for fixed blockage ratios.