Evolution of a shock-impacted reactive liquid fuel droplet with evaporation effects: A numerical study

Abstract

We describe detailed numerical simulations of a liquid fuel droplet impacted by a Mach 5 shock wave, considering the effects of chemical reactions and phase change due to evaporation. In our baseline case, a 5μm, n-Dodecane fuel droplet is preheated to 460K, and surrounded by preheated O2 gas at 700K. The simulations investigate the low Ohnesorge number regime (Oh<0.1), where viscous effects are insignificant and therefore not considered in this work. The fuel droplet undergoes significant deformation and morphological changes following shock impingement, as the droplet surface becomes unstable to the Kelvin-Helmholtz instability. The droplet core is also observed to eject a thin sheet near the equatorial plane, which is then stretched by the high-speed post-shock gas flow, affecting the late-time behavior. We find the observed dominant modes associated with the Kelvin–Helmholtz instability are in reasonable agreement with inviscid linear theory (Chandrasekhar, 1981; Jepsen et al., 2006), when the local conditions at the droplet surface are considered. Furthermore, an evaporation-induced Stefan flow is established which blows off the hot post-shock gases surrounding the droplet, leading to droplet cooling. As the fuel vapors react, a diffusion flame is formed on the droplet-windward side, leading to intense droplet heating and enhanced vapor production in this region. We investigated the effect of the Damkohler number on droplet evolution by varying the fuel reactivity, and found the flame thickness decreased with increasing reactivity in agreement with trends predicted by laminar diffusion flame theory. At the highest reactivity, secondary burning of fuel vapors was observed in the droplet wake, while the resulting flame eventually reattached to the droplet surface. Our results show significant spatial inhomogeneities are present in the droplet flowfield in all the cases investigated, which must be considered in the development of reduced order point-particle models for system-level simulations of detonation engines.