Deformation and acceleration of small droplets at high-speed conditions

Shock-driven droplet breakup occurs in various physical systems and plays a critical role in emergent high-speed flight applications such as droplet combustion in rotating detonation engines (RDEs) and droplet impacts on hypersonic vehicles. Droplets interact with strong shock waves in these applications, and the high post-shock gas velocity and temperature lead to rapid droplet acceleration, evaporation, and breakup through various hydrodynamic instabilities. Accurate prediction of the breakup process is essential in these applications and theory-based models are required to cover the large parameter space encountered. In order to model the growth of hydrodynamic instabilities on the droplet, the acceleration and droplet shape must be known first, requiring accurate prediction of both deformation and drag. Previous work has largely focused on large droplets at lower shock strengths, where acceleration and evaporation are much slower. Here, the dynamics of small droplets accelerated by strong shock waves are explored up to the onset of breakup, focusing on droplet size, Mach number, and evaporation effects on the deformation and acceleration.

Shock tube experiments are conducted for a wide range of parameters including droplet size, shock strength, and liquid properties. Incident shock wave Mach numbers of 1.35 - 2.1 are used with micron-scale droplets with diameters from $\sim 50$ to $200\left[\mu m\right]$. Various fluids (water, dodecane, and acetone) were studied yielding Weber numbers from $\sim 100\text{–}6000$. Droplet deformation and position are measured with sub-micrometer spatial resolution and sub-microsecond temporal resolution. New modifications to the Taylor Analogy Breakup model are presented with modified drag correlations accounting for deformation and Mach number effects to accurately capture the droplet dynamics. The results are compared with previous millimeter-droplet breakup studies, finding that bulk droplet deformation and drag are captured by the new models over a wide range of conditions. Evaporation was not observed to effect these processes, even for the smallest droplets. However, small droplets are shown to exhibit significantly less hydrodynamic instability growth than large droplets, which display a larger departure in trajectory from the model at late times.