Mathematical Modeling of the Ejected Droplet Size Distribution in the Vicinity of a Gas–Liquid Impingement Zone

Abstract The controlled splashing of metal droplets plays a decisive role in the kinetics of the basic oxygen furnace (BOF) process. In this work, a mathematical model was developed for predicting the size distribution of spherical droplets ejected at an impingement zone. Harmonic oscillators are used to describe the ejection sites, and the upper limit for the droplet population is calculated through a force balance. The model was validated against literature data from high-temperature crucible experiments involving different supply pressures and lance heights as well as both single-hole and multihole lances. The predicted size distribution of the metal droplets was found to be in good agreement with the droplet size distributions measured from outside the crucible. The model was also applied for predicting the size distribution parameters of the Rosin–Rammler–Sperling (RRS) size distribution function. The model developed is computationally light and is suitable to be used as a part of offline and online simulation tools for the BOF process.