Error analysis and optimization of the coupled volume of fluid and Lagrangian particle tracking method for liquid jets in crossflow simulations

The transformation criterion is critical for the coupled volume of fluid and lagrangian particle tracking (VOF-LPT) method for jet breakup and atomization simulations, which determines the conversion from VOF droplets to Lagrangian particles. It is usually developed based on experience, varies among researchers (e.g., different maximum transformation diameter), and consequently leads to considerable computational errors. To mitigate such errors in simulations of liquid jets in crossflow (LJCF), an optimized transformation criterion of the VOF-LPT method was developed and validated in this study. First, a comprehensive parametric study of a two-dimensional LJCF case was conducted to investigate the primary breakup process. It was found that liquid column deformation was more sensitive to mesh resolution than to interface capturing methods, and a minimum of 32 cells across the jet diameter was essential to accurately capture the periodic deformation characteristics. Second, the secondary breakup process was studied through detailed three-dimensional simulations of droplets in crossflow. An optimized transformation criterion was developed based on quantitative error analysis of the droplet displacement of VOF and LPT methods. It was established based on the local droplet Weber number and local mesh resolution, and without any coefficient that needs calibration. Finally, the proposed criterion was validated using a three-dimensional LJCF case, demonstrating a remarkable improvement of over 30% in droplet size prediction accuracy compared to conventional implementations based on the maximum diameter criterion.