Simulation of Primary Film Atomization Due to Kelvin–Helmholtz Instability

Abstract

Liquid film atomization under a high-speed air flow (water was considered as the liquid) due to the Kelvin–Helmholtz instability is studied using the volume of fluid (VOF) method. We develop an approach for modeling the primary breakup and use it to investigate the grid convergence, choose the optimal size of the grid cell, and calculate the primary breakup of the film in the channel. The dependences of the mean break-off angle, the velocity modulus, and the Sauter droplet diameter on the longitudinal coordinate of the channel are obtained. The step-by-step averaging over the ensemble of droplets and over time allows us to get smooth coordinate dependences of the characteristics of the ensemble of the droplet. The value of the most useful parameter for engineering applications, the mean Sauter diameter D₃₂ (equal to the ratio of the mean droplet volume to its mean area) is close to that obtained using a semiempirical formula from the literature, based on the experiment where hot wax is atomized by a high-speed airflow. The dependence of the Sauter mean diameter on the thickness of the liquid layer agrees qualitatively with the experimental dependence. The study of the grid’s convergence showed that the number of the smallest droplets increases rapidly with decreasing cell size. Their contribution to the average characteristics of the droplet’s ensemble, however, remains insignificant; nonetheless, their input to the mean characteristics remains insignificant; thus, there is no reason to decrease the grid cell size to account for small droplets.