Experimental investigation of momentum ratio and Weber number influence on droplets’ characteristics for jet in cross-flow

In this study, the droplet size and velocity distributions resulting from liquid jet and sheet injections into a cross-flow were investigated. Since previous research has provided limited insights into the effects of rectangular nozzles compared to circular ones, this study tested four different nozzles – two circular and two rectangular – each with distinct hydraulic diameters. This design aimed to explore the influence of nozzle geometry and hydraulic diameter on droplet size and velocity distributions. To assess the effects of liquid and gas flow conditions on the microscopic properties of droplets, the cross-flow Weber number ranged from 6 to 15, while the injection fluid Weber number varied from 90 to 1100. Additionally, measurements were conducted at varying distances and spatial positions relative to the spray nozzle, capturing three-dimensional spatial distributions of the studied parameters. An experimental methodology was employed to measure droplet size and velocity. The test setup was equipped with high-precision imaging capabilities and the shadowgraphy technique was utilized for droplet visualization. The collected data were analyzed using data analysis approaches, including analysis of covariance, multiple linear regression, and standard statistical tests. The investigation into the effects of flow conditions on droplet size revealed that the momentum ratio between the injected fluid and the cross-flow plays a critical role, with higher momentum ratios resulting in smaller droplet sizes. Furthermore, the study identified a critical gas Weber number and a universal critical momentum ratio, highlighting a dual-effect mechanism of the cross-flow on droplet diameter. This novel finding and its underlying physics, to the authors’ knowledge, have not been explicitly reported in prior research. The analysis also demonstrated that increasing the Weber number of either the injected fluid or the cross-flow increases the velocity of the produced droplets. A general inverse relationship between droplet size and velocity was observed. Regarding nozzle effects, the results indicate that rectangular nozzles produce smaller droplets, while larger hydraulic diameters yield larger droplet sizes. Finally, power-law relationships were developed to describe the distributions of droplet size and velocity as functions of flow conditions and spatial position for each nozzle type.