  The Eulerian-Lagrangian method is applied to simulate pulsating propagation
and extinction of stoichiometric hydrogen/oxygen/argon detonations in ultrafine
water sprays. Three detonation propagation modes are found: (1) pulsating
propagation, (2) propagation followed by extinction, and (3) immediate
extinction. For pulsating detonation, within one cycle, the propagation speeds
and the distance between reaction front (RF) and shock front (SF) change
periodically. The pulsating phenomenon originates from the interactions between
gas dynamics, chemical kinetics, and droplet dynamics inside the induction
zone. Multiple pressure waves are emanated from the RF within one cycle, which
overtake and intensify the lead SF. An autoigniting spot arises in the shocked
gas after the contact surface. The relative locations of SF, RF, shock-frame
sonic point, and two-phase contact surface remain unchanged in a pulsating
cycle, but their distances have periodic variations. Moreover, the unsteady
behaviors of detonation extinction include continuously increased distance
between the RF and SF and quickly reduced pressure peaks, temperature, and
combustion heat release. The decoupling of RF and SF leads to significantly
increasing chemical timescale of the shocked mixture. The hydrodynamic
structure also changes considerably when detonation extinction occurs.
Moreover, the predicted map of detonation propagation and extinction
illustrates that the critical mass loading for detonation extinction reduces
significantly when the droplet size becomes smaller. It is also found that for
the same droplet size, the average detonation speed monotonically decreases
with water mass loading. However, detonation speed and pulsating frequency have
a non-monotonic dependence on droplet size under a constant water mass loading.
