Direct initiation of hydrogen detonation in fine water sprays

Understanding the direct initiation of detonation is crucial for developing effective detonation inhibition strategies. We numerically investigate the direct initiation of hydrogen/air detonation in a circular water cloud using the Eulerian-Lagrangian method with two-way gas-droplet coupling. Parametric analyses demonstrate that both droplet concentration and cloud radius have significant effects on peak pressure trajectories of the detonation wave. Three direct initiation modes of detonation in fine water sprays are observed: supercritical, critical, and subcritical. These modes are identified based on the triple point trajectories and the evolutions of local shock speeds. In critical initiation, the characteristic scales for the gas-droplet two-phase detonation are plotted. Analyzing the gas temperature and chemical timescale reveals that critical initiation involves three phases: overdriven detonation due to strong blast wave, detonation decoupling resulting from fine droplets with high evaporation rates, and detonation re-initiation induced by focusing of transverse detonation waves, as well as its decaying to approach the Chapman-Jouguet speed. Furthermore, subcritical initiation generally has overdriven detonation followed by detonation decoupling, featured by quickly fading peak pressure trajectories. This is because the triple points and transverse waves are weakened by two-phase exchanges and cannot directly initiate gas reactions. The influence of water cloud characteristics, including droplet evaporation rate, temperature, diameter, and Weber number, is explored. Results show four distinctive zones of the water cloud in the two-phase detonation initiation: pre-evaporation, low evaporation rate, high evaporation rate, and central evaporation. It is also demonstrated that the shocked cloud initially expands outwardly and then shrinks. The low-evaporation-rate zone first vanishes, followed by the outer cloud, while the inner cloud persists until the final stage. The droplet behaviors follow Pilch and Erdman model.