Unraveling Spray Dynamics and Droplet Generation from an Energy Perspective*

The droplet size distribution of sprays is influenced by numerous factors, including nozzle design, source pressure, working fluid properties, and external flow. Despite this complexity, sprays are governed by a straightforward energy balance, where the driving fluid power is partitioned into the rate of surface energy production associated with droplet formation, the viscous dissipation rate, and the droplet kinetic energy rate. While the surface energy term is commonly normalized to yield the spray efficiency, the latter kinetic energy term is more sparingly estimated. The kinetic energy of individual droplets influences droplet transport through quiescent air and droplet impact outcomes, which are particularly of interest in agricultural sprays, internal combustion fuel injectors, and spray coatings. Herein, we estimate droplet kinetic energy and develop a scaling relationship in terms of input spray parameters. Digital inline holography (DIH), combined with a novel machine learning based post-processing method for data extraction, is used to measure the spatial distribution of droplets and their temporal evolution. From this high-fidelity data obtained using DIH on different nozzles at three distinct locations—the center, half-span, and edge of flat fan sprays—under different tank pressures, we are able to estimate the kinetic and surface energy. This study aims to enhance understanding of energy distribution in sprays and optimize spray systems across applications.