Droplet breakup and evaporation in liquid-fueled detonations

In liquid-fueled detonations droplets are subjected to a myriad of complex codependent physical phenomena occurring on overlapping temporal and spatial scales, resulting in rapid vaporization. The rate at which droplets vaporize is enhanced by the concurrent hydrodynamic breakup processes. This article describes experiments where small ($d<125\mu m$) droplet breakup at high Weber number $O\left(10^4\text{–}10^5\right)$ is imaged in a self-sustained liquid-fueled detonation with laser optical Mie scattering imagery. Experimental initial conditions, including the droplet size and mass distribution, are characterized and reported. Child droplet clouds generated from droplet interactions with detonation waves are observed to persist for approximately 10 mm past the detonation front and grow to the order of millimeters in width. A velocity deficit of $\sim 10\text{\%}$ was observed for the multiphase detonations wave speed when compared to calculations for the equivalent gaseous detonations. The bulk droplet survival distances and breakup cloud morphology are compared to the predictions of relevant evaporation and breakup models. Calculations indicate that evaporation alone would result in droplet survival distances orders of magnitude longer than those observed. A droplet process whereby breakup occurs over an extended time, concurrent with evaporation, provides a phenomenological explanation. Empirical models constructed for shock-driven breakup predicted larger child droplet sizes than theoretical models based on linear stability theory, yielding survival distances and cloud shapes within the range of values seen in experiments. Droplets were however observed to persist longer than either model would predict. The discrepancy between calculations and experiment indicate that development of models tailored to droplets subject to variable acceleration are necessary to fully explain the multiphase detonation.