Droplet Size Spatial Distribution Model of Liquid Jets Injected into Subsonic Crossflow

Liquid jet injected into transverse subsonic gaseous flow has been widely utilized in many industrial applications. It is useful to determine the spatial distribution of generated droplets in the near-field region for high-efficiency combustion. In this paper, we propose a simplified model to predict droplet spatial distribution in transverse subsonic gaseous flow. Linear stability analysis has been used to determine the disturbance growth rate on the surface of a liquid column. When the amplitude of disturbance is of the same order of magnitude as jet radius, the liquid jet breaks up into ligaments. We can make an assumption that the generation rate of small droplet equals to liquid breakup rates, which varies with a spatial location under this circumstance. Combining these relations with the definition of SMD (Sauter mean diameter), a semitheoretical relation to evaluate droplet spatial distribution along the liquid column can be established. The present model has been compared with empirical relation based on experiments under different conditions. Results indicate that in the surface breakup region, the current model shows great consistency with experimental observations while there exists a relatively large discrepancy between the current model and experimental observation in the column breakup region because of its strong nonlinear effect near the breakup point. In addition, the effects of flow parameters on droplet size spatial distribution have been investigated.