Two-dimensional (2D) numerical simulations based on Eulerian-Lagrangian method are conducted to clarify the droplet behavior within its lifetime within the detonation cell. The simulation results are analyzed via 2D instantaneous flow fields and Favre spatiotemporal average technique, by applying the recycling block method. Gaseous detonation with dilute water droplets (WDs) propagates stably with a 4% velocity decrease compared to dry CJ velocity in the simulation conditions. From the instantaneous flow field analysis, the droplet breakup occurs primarily in jets, downstream of the transverse wave, nearby the collision of transverse waves, and the interaction between the transverse wave and the jets. The Favre average one-dimensional profiles by grouping WDs based on the initial shock strength that WDs experience reveal the droplet life inside the cellular structure. The mean equilibrium diameter after the breakup is not affected by the initial shock strength.