Detonation mode and frequency analysis under high loss conditions for stoichiometric propane-oxygen

The propagation characteristics of galloping detonations were quantified with a high-time-resolution velocity diagnostic. Combustion waves were initiated in 30-m lengths of 4.1-mm inner diameter transparent tubing filled with stoichiometric propane–oxygen mixtures. Chemiluminescence from the resulting waves was imaged to determine the luminous wave front position and velocity every 83.3 μ. As the mixture initial pressure was decreased from 20 to 7 kPa, the wave was observed to become increasingly unsteady and transition from steady detonation to a galloping detonation. While wave velocities averaged over the full tube length smoothly decreased with initial pressure down to half of the Chapman–Jouguet detonation velocity (D_CJ) at the quenching limit, the actual propagation mechanism was seen to be a galloping wave with a cycle period of approximately 1.0 ms, corresponding to a cycle length of 1.3–2.0 m or 317–488 tube diameters depending on the average wave speed. The long test section length of 7300 tube diameters allowed observation of up to 20 galloping cycles, allowing for statistical analysis of the wave dynamics. In the galloping regime, a bimodal velocity distribution was observed with peaks centered near 0.4 D_CJ and 0.95 D_CJ. Decreasing initial pressure increasingly favored the low velocity mode. Galloping frequencies ranged from 0.8 to 1.0 kHz and were insensitive to initial mixture pressure. Wave deflagration-to-detonation transition and detonation failure trajectories were found to be repeatable in a given test and also across different initial mixture pressures. The temporal duration of wave dwell at the low and high velocity modes during galloping was also quantified. It was found that the mean wave dwell duration in the low velocity mode was a weak function of initial mixture pressure, while the mean dwell time in the high velocity mode depended exponentially on initial mixture pressure. Analysis of the velocity histories using dynamical systems ideas demonstrated trajectories that varied from stable to limit cycles to aperiodic motion with decreasing initial pressure. The results indicate that galloping detonation is a persistent phenomenon at long tube lengths.