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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. [ABSTRACT FROM AUTHOR]

One-dimensional numerical simulations based on the hybrid Eulerian–Lagrangian approach are performed to investigate detonation dynamics in two-phase gas-droplet n-heptane/air mixtures with and without liquid fuel pre-vaporization. The reactive Navier–Stokes equations considering the two-way coupling for interphase exchanges of mass, momentum, energy, and species are solved with a skeletal mechanism consisting of 44 species and 112 reactions. The effects of n-heptane droplet diameter and equivalence ratio (ER) on average detonation speed and mode are studied. For pre-vaporization cases, the average detonation speed first decreases and then increases with droplet diameter ranging from 2.5 to 40 μm, which is minimum at 7.5–10 μm due to the competition between fuel vapor addition and droplet evaporative heat absorption. However, the average speed increases monotonically as the droplet ER increases from 0.2 to 1.2. A further increase in the droplet ER (e.g., 2.4) would lead to detonation suppression in the presence of large droplets (e.g., above 30 μm). The detonation is fully quenched when the droplet ER is 3.2. Similar observations are also made for the pure sprayed cases without n-heptane pre-vaporization, where the average speed increases rapidly for droplet ER of 0.2–0.8 and slowly for ER of 0.8–1.6. Various detonation modes are observed with respect to droplet diameter and equivalence ratio, either with or without fuel pre-vaporization. Generally, the pure sprayed cases show more irregular behaviors in detonation propagation. The laden droplets provide a new approach to control the intrinsically unstable or highly irregular behaviors of pure gas or pure sprayed detonations. The finite, small disturbances from the spatially non-uniform droplets, and enrichment from the droplet evaporative mass addition, are two essential mechanisms for the mitigation of the pulsating detonation. [ABSTRACT FROM AUTHOR]

The interactions between an incident shock and a moderately dense particle curtain are simulated with the Eulerian–Lagrangian method. A customized solver based on OpenFOAM is extended with an improved drag model and collision model and then validated against two benchmark experiments. The results show that the collision model has a limited impact on curtain morphology compared with the improved drag model. In this work, parametric studies are performed considering different particle sizes, volume fractions, and curtain thicknesses. Smaller particle sizes and larger volume fractions lead to stronger reflected shock and weaker transmitted shock. Attention is paid to the particle collision effects on the curtain evolution behaviors. According to our results, for the mono-dispersed particle curtain, the collision effects on curtain front behaviors are small, even when the initial particle volume fraction is as high as 20%. This is due to the positive velocity gradient across the curtain after the shock wave passage, leading to the faster motion of downstream particles than the upstream ones, and hence, no collision occurs. For the bi-dispersed particle curtain, the collision effects become important in the mixing region of different-size particles. Collisions decelerate small particles while accelerating large ones and cause velocity scattering. Moreover, increasing the bi-dispersed curtain thickness leads to multiple collision force peaks, which is the result of the delayed separation of different particle groups. Our results indicate that the collision model may be unnecessary to predict curtain fronts in mono-dispersed particles, but in bi-dispersed particles, the collision effects are important and, therefore, must be modeled. [ABSTRACT FROM AUTHOR]