Numerical modelling of liquid-fuelled detonations in tubes

A numerical model for liquid-fuelled detonation is developed. An Eulerian-Lagrangian formulation with two-way coupling between the gas and droplet phases is used to numerically simulate detonation of JP-10 fuel droplets in O-2 in a 1.5 m tube. The results of spatial and temporal resolution studies are presented. Then, the consequence of various choices of droplet drag and convective-enhancement sub-models is investigated. It is found that the detailed effects of such models are secondary to those of chemical energy release of the detonation. Detonation structure is shown to vary with initial droplet size and with the amount of initial fuel vapour present. For the range of small droplets considered, the self-propagating detonation velocity depends only minimally on such parameters. Small deficits in propagation velocity from the gaseous Chapnian-Jouguet (C-J) value appear to be due to increasing inhomogeneity of the fuel-oxidant mixture as droplet size increases. Such results are in general agreement with the limited experimental data available. Also comparable to experimentally observed trends, results show that the existence of some initial fuel vapour increases the ease of detonability of liquid-fuelled mixtures. More generally, smaller droplet sizes and higher levels of heating and prevaporization are shown to enhance quick transition to a sustained self-propagating detonation.