  In this study, a numerical investigation based on the Eulerian-Lagrangian
model is conducted to explore a rotating detonation engine (RDE) fueled by
liquid ethanol. The focus is on examining the characteristic phenomena of the
two-phase rotating detonation wave (RDW) caused by droplet evaporation and
varying inlet conditions. To enhance the evaporation of liquid fuel, pre-heated
air is used, and both liquid and pre-vaporized ethanol are simultaneously
injected. The distribution of ethanol droplets reveals an initial concentration
near the injection surface and accumulation in the fuel-refill zone. Here,
liquid droplets gradually evaporate after absorbing latent heat from the
surrounding gas. The subsequent interactions between the evaporating droplets
and the RDW vary with the droplet size. For droplets with diameters of $d_0$ =
5-15 $\mu$m, after being swept by the RDW, a secondary evaporation process
occurs, leading to an enlargement of the width of the reaction zone. However,
the chemical reactions still predominantly take place in close proximity to the
detonation front. As further increases, droplet evaporation persists in the
post-detonation expansion zone over a long distance until the remaining
droplets are fully evaporated and eventually burned in this region. The study
also analyzes the extinction of rotating detonations and the emergence of new
detonation waves resulting from local explosions and consequent shock
collisions. It is demonstrated that variations in the diameter of injected
droplets and inlet temperature can lead to different operating modes with
varying numbers of RDWs.
